I'm trying to animate a 3D curve, and I was hoping that someone might push me in the right direction...

My User Story:

1. I have a sphere
2. I've defined 2 points on the sphere using spherical coords
3. I want to connect those two points with a curve
4. The curve has a beginning and an end
5. The curve would be drawn over time
4. It would resemble a flight path

Up till now, I've been drawing my curve with a Bezier. But it seems that this approach is problematic for a couple reasons:

** the control points I pick are only eye-balled approximations to the sphere, b/c they aren't real spherical coords

** is it even possible to animate Bezier curves as described in my User Story

Should I be pursuing a different curve? Is gluNurbs something that I should look into instead? Or if Bezier curves are perfectly valid, I'll dig deeper. I just want to make sure I'm looking in the proper direction.